The Nature of Measurement: Part 12: Universal Truths Found in Measurement Science

After years of reflecting on measurement, I have discovered some axioms or maxims imbedded in its essence. An axiom is an accepted principle, proverbial truth or maxim. A maxim is a general truth, moral reflection or rule of conduct. Whatever word chosen to describe them, there are universal truths at the heart of surveying, and they are applicable to any situation at any time.

Being preoccupied with measurement science has contributed significantly to my understanding of life's events and provided a flow of insight regarding choices and reactions to various situations involving human interaction. Studying measurement science has helped me learn more about life and relating to the world than have many books on human behavior. The philosophies and applications outlined in such books generally suffer from the limited experience and perspective of their writers. However, measurement science concepts apply universally, are self evident and leave little room for debate. When something can be seen as an axiom or maxim, we waste our time with opinion and intellectual reasoning about it. The Holy Bible, particularly books such as Proverbs, is the only written source that has been more significant for me than the science of measurement for gaining insight to guide my behavior and my reaction to the behavior of others.

This last article in the series on the nature of measurement explains how, with ample study and reflection on the nature of measurement, one can see truths that have little to do directly with surveying or measurements, but which can be applied in just about any situation being evaluated or considered. It is my desire that others gain as much as I have from this body of knowledge. I hope the following will help you along your journey.

Axiom #1: We are responsible for our mistakes.

In measurement, we learn that errors and mistakes are not the same. Errors are unavoidable. Mistakes are generally caused by carelessness, inattention, lack of information, poor training, negative and uncontrolled emotions and so forth, and thus are avoidable. Unless mistakes are either avoided or corrected promptly, there will be inevitable consequences. The consequences are usually cost, inconvenience, damage or pain for someone, whether dealing with measurements or something else. Thousands of lawsuits undoubtedly occur daily because people have been damaged by mistakes.

The very nature of mistakes requires us to take responsibility for them. Understanding this should help anyone see that rationalizing any mistake away is unacceptable. It teaches further that the best way to deal with mistakes is to avoid them by being careful and attentive, gaining the right education or training, staying current as to the knowledge required to execute tasks or practice our chosen profession, keeping sober and in control of our thoughts and movements and maintaining a positive and professional attitude. This aspect of life, learned by application of elementary measurement science, is universal. Taking responsibility for mistakes is a sign of a professional attitude and a mature and emotionally healthy individual or society.

Axiom #2: Truth is approached whenever we take our initial observations and modify them using corrections gained by knowledge of where we were in error initially.

In measurement science, we simply say:

True Value = Reading + Sum of Corrections

OR

(T = R + C_T)

When dealing with measurements, we are confronted with the reality that accuracy cannot exist unless the systematic errors are sought, found, evaluated and corrected or compensated. Human perceptions and readings of measurements in surveying are just part of a larger universe, which we can call observations. Without corrections, observations of any kind, and of any phenomena, are merely biased perceptions that may be far from the truth. In any event involving human interaction, our perception is inevitably biased or confused by emotions or preconceived ideas, manipulation of our emotions by propaganda or drama, deliberate or sloppy reporting of facts, lack of research into the facts, lack of relevant evidence, or lack of background education that would provide the knowledge of the theory and principles and the ability to think analytically. Knowledge has a natural way of helping remove bias. Truth has a way of setting us free from prejudices and misconceptions that block the view of accuracy.

As for human perceptions, our ego and pride often get in the way, and we readily and often unquestioningly decide and declare that the initial perception gained from the observation is accurate. The way of a fool always seems right to him. We often do not want to be "confused with facts" and resent it when more complete evidence surfaces that dictates a mind change or alteration of the proposed solution to the problem. One's reaction, when confronted with the facts (systematic errors) can include anger, defensiveness, vindictive behavior or denial. Often, the result is rigid adherence to the biased perception adopted and owned by the individual, with probable upset of some relationship.

If I understand and accept the aspect of measurement science embraced by this axiom, I will always question my own and others' perceptions, knowing they are undoubtedly biased. This assumes, of course, that my quest in life is to ascertain the truth. If it is to gain something personally, find the easy way or try to look good in the eyes of others (play "politics"), then no amount of knowledge in this regard will help me get closer to the truth. If truth is the goal, I am not afraid to alter my initial observation. I know, from this universal truth of the way things evolve, that it is normal, inevitable and necessary to often change my initial perceptions.

Axiom #3: Our perceptions are inexact, whether of measured quantities or other subjective phenomena.

This axiom relates to random errors, which lurk beneath the surface and frustrate any arrival at truth through observation. Therefore, regarding the equation cited under Axiom #2, I must modify the theory with the reality that I only approach, rather than find, the true value.

Some biases are unknown or difficult to detect. If we knew what they were, they would be systematic and therefore removable. All of our judgments, no matter how carefully considered, are flawed. This may come as a shock to some people, but this condition cannot be denied. Once we fully accept this, we begin to see that the judgments of others might be as good as our own, or at least we begin to consider that possibility. In discussions or debates of all types, we can get more outside of our own little world and weigh everyone else's comments. This universal truth can help to develop humility, objectivity and an attitude of cooperation and compromise.

When this axiom is fully understood and placed into operation, we can cease to expect perfection from employees, the guy driving the car in front of us, our spouse, ourselves or anyone. We will eventually tend to blame less and seek solutions or resolutions instead. As we see the scatter in numerical values of surveyed data, it should constantly remind us of the wide range of well-considered opinions regarding subjective data and to entertain the possibility that any one of these observations could be as close to the truth as any other. The fact that one of the observations happens to be our own, or that many may agree on an issue, doesn't create truth.

Axiom #4: Agreement of the majority is insufficient to declare that the best solution has been decided.

This axiom stems from the concepts of precision and accuracy. Reflecting on the two concepts helps us understand why it is important to distinguish between them and that they apply to everything, not just measurements. As we learn in surveying, precision relates little to accuracy. For instance, making several repetitions of a measurement, or closing a survey on itself, finds a few possible mistakes and helps evaluate precision. However, it does not detect systematic errors and therefore does not adequately check accuracy.

Earlier in this series I defined accuracy in measurements as adherence to defined standards on weights and measures, geometric laws or accepted datums. In affairs outside of measurement, accuracy isn't so easy to define. I will simply say that it is that which adheres to accepted legal, ethical or moral standards. It is what wisdom suggests would benefit others and not selected factions or groups having motives based in fear and other forms of self interest. Accuracy, as a measure of quality or what is "right," checks observations against something outside of the self or a small group, the something representing an absolute standard and ideally being free of bias.

Unfortunately, the truth is always elusive. Precision is much easier to observe. It requires only checking something against itself (usually our own work) or against similarly biased observations rather than a higher, outside standard. Making comparisons and weighing things against standards outside of ourselves is probably one of the hardest things for anybody to learn and to do consistently. Perhaps this is why precision is so often confused with accuracy when it comes to evaluating measurement quality in surveying.

In a court of law, the collective strength of evidence gained by the testimony of several witnesses is sufficient to gain a preponderance of evidence or prove an issue beyond a reasonable doubt only if each testimony is given independently, without collaboration, and if the witnesses are unprejudiced in their testimony. If each person gives "the truth and nothing but the truth," then a relatively few witnesses can be effective in proving a point. Truth will be obvious when the testimony is unbiased and unswayed by fear, temptation, greed and so forth. But, if witnesses successfully conspire to testify untruthfully but with a consistent story, justice will not be served. We have precision without accuracy.

A wise person seeks many counselors or consultants when trying to clarify an important issue or decide a course of action. Unfortunately, if all of the consultants are similarly biased, the counsel may not lead to the best decisions. If many people consulted have fears, prejudices, biases or self interests (often the same ones as the seeker), the collective advice may result in actions that are illegal, unethical, immoral and thus not "right." This can happen even if there was no deliberate attempt to manipulate everyone to agree according to some self interest. It occurs simply because the person is not wise enough to consult people who might disagree with his or her preconceived notion or pet project. Most of us are guilty of seeking support only from people who we anticipate are going to agree with us and avoiding contact with those who we suspect will not agree. Thus, we surround ourselves with many like-minded people and, being fed by the confidence we get from this selected and biased group, begin to feel in time that we must be "right." Hopefully, the insight gained from this axiom will help us know the best sources of counsel.

As an example of the above failure, I have observed countless times, in professional meetings and matters, how issues are pushed by people who feel they must be right because so many people seemingly agree with them. The "good old boy" organizations that surveyors call professional associations are often guilty of this. Members who often have genuine vision and goals based on serving the public and strengthening the profession are often ignored, ostracized and discouraged to the point of dropping out of the associations as the "status-quo" people band together into an unmovable and unchangeable core wallowing in a sea of fear and bias.

Another example of how repeatability has affected the strength of our profession is how the content of the NCEES examinations for land surveyors has been decided over the last 25 years. The tasks surveyors perform, based on return of thousands of questionnaires, have been used to decide exam content. If the majority did not use or apply a procedure, the subject matter was either omitted or greatly de-emphasized on the exam. That it might better protect the public if surveyors were expected to have certain knowledge and apply certain technical procedures has not been a factor in deciding the exam content. The knowledge base of the majority of the practitioners and the level of their practice has been the deciding factor. The system has emphasized the collective opinion of the majority, thus focusing on precision rather than what might be best.

There are countless examples of how precision without accuracy changed the course of history. Adolf Hitler's vast following for many years is one. The Watergate scandal during President Nixon's term of office is another. One of those involved in that scandal said that (paraphrased) someone needed to stop and ask "is this right," and they may have been able to stop what happened. This man recognized, too late perhaps, that they were a closed group whose collective opinion was not centered on truth.

We should always look for repeatability or agreement among wise people whose motives are unselfish or not biased in any particular political direction. Repeatability, when sought in this way, validates. Nonetheless, just as closing a survey on itself does not ensure accuracy, a large number of people agreeing on something does not in itself make it right.

Another lesson we can learn from all of this is that to disagree with the majority may be the right thing. Some non-conformists often have a point.

Axiom #5: Imperfection lies within the finite dimensions of humankind, whereas perfection is found at the infinite dimension.

We approach zero error or ultimate precision as we approach infinity. This is illustrated by the relationship between the error in a single value and the error in the mean of a large number of repetitions of a quantity. The error in the mean of a set of observations in a measuring procedure is equal to the standard deviation for the procedure divided by the square root of the number of observations in the set.

Perfection is found at infinity because the square root of infinity is still infinity and anything divided by infinity is zero. No matter how many times I repeat an angle, I cannot resolve it to zero error because I must operate with a finite number of observations.

Can we mortals find perfection in anything? This axiom, based on measurement science and mathematics, teaches us that we cannot. I have not yet met a person or group on this planet who has absolutely accurate and consistently correct judgments on all matters. The error in any individual or collective judgment or decision made by humans is short of perfection, no matter how long we ponder the situation or how many experts we consult.

The value of seeking many counselors, as discussed in the previous section, is driven home with this axiom. It teaches that if we seek the opinions and judgments of many, we will probably make wiser decisions. Although we cannot ever know what is "right," we can do better by seeking more opinions. Of course, the opinions, if used (they can be rejected), must be based on objective thought and evaluation of the evidence; otherwise "wild values" contaminate the sample. Wise people rarely make important decisions about anything having significant potential consequences without consulting various reliable sources. A wise man listens to counsel. Plans succeed with many advisors because the error in the judgment is reduced by the square root of the number of unbiased experts consulted. Likewise, plans are more apt to fail when made alone. The square root of one is always one.

Axiom #6: Absolute certainty is impossible in the real world. Certainty is delusion, whereas uncertainty is reality.

Remember the bell curve? The standard deviation, occurring at the points of inflexion, is the 68.3 percent level of certainty. To gain more certainty, we must widen the range of error. To have 100 percent certainty in anything measured, the range of error or the tolerance must be infinitely large. Statistical analysis and this curve teach us this.

From the above, we realize that 100 percent certainty is not possible in the real world where human judgment or perception is involved. This is true regarding both measurement science and personal decisions.

The truly open-minded person is uncertain. This is a conclusion we must reach after considering the above. As we ponder all of this, we begin to realize that certainty inevitably leads to rigidity and closed-mindedness, where new evidence is difficult to consider or accept, with consequent unwillingness to modify perceptions to further approach truth. Indeed, a fool is one who ignores facts, is not open to evidence or new knowledge, has his mind "made up," makes decisions with insufficient information or simply leans on his limited understanding.

Well-balanced people seem to know instinctively that they do not have the luxury of an infinitely large tolerance and so have some reservations or doubt about any decision. It is healthy to have self confidence when judgments are well considered, but some measure of caution and doubt is healthy too. I can proceed in a matter as an act of faith, but faith, by definition, is not susceptible to such analysis.

I remember that when I was a young Army lieutenant in training, the training officer would ask (right in my face) "Are you sure, Lieutenant?" I was trained to reply "Yes, Sir!" I was lying, of course. But I couldn't answer, "I am 99 percent sure." It wouldn't have been acceptable, and it would have been at least 90 percent certain that I would be doing push-ups had I replied with anything other than an absolute "Yes, Sir!"

We have been conditioned to expect the "Yes, Sirs" from our peers, our political leaders, our children, our spouses, our employees and so forth. The certification on your survey plat is a statement of 100 percent certainty. The law will use it against you later, declaring, "You said it was so."

Somehow, we have had it all wrong. We make a serious mistake when we expect certainty from ourselves or others. We should begin admitting uncertainty. It is more honest. This may go contrary to the way we are taught by parents, employers, politicians and peers. Nonetheless, it is true because we operate within finite dimensions.

Living with uncertainty may frighten some people. However, when the alternatives and the consequences of closed-mindedness and rigidity are considered, uncertainty becomes therapeutic. It is the route to better solutions and improved personal and other relationships, so it is bound to ultimately make a person feel better than always being certain.

Summary

Hopefully, this last in the series on the nature of measurement will give readers a deeper appreciation of our profession and the ability to tap into a source of insight and wisdom perhaps not recognized before. When you probe into the nature of measurement, the theory, concepts and equations begin to be seen as a mirror of life itself.

This exploration focused on the science of measurement. Before leaving here, I must say that there is more insight to be gained from a similar consideration of that other aspect of our professional thinking—that of evaluation of evidence and the role of the land surveyor in retracement. However, this aspect was completely omitted here for lack of space and the desire to focus on one theme. Maybe some other time we can tell "the rest of the story."

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